A computer program to solve geometric programming problems: an illustration using Rijckaert and Martens' Problem 6 [76]

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below aims to solve the following geometric programming problem based on Problem 6 on page 229 of Rijckaert and Martens [76, p. 229]:

Minimize

- ( -2 * X(1) ^ .9 * X(2) ^ -1.5 * X(3) ^ -3 - 5 * X(4) ^ -.3 * X(5) ^ 2.6 - 4.7 * X(6) ^ -1.8 * X(7) ^ -.5 * X(8) )

subject to

7.2 * X(1) ^ -3.8 * X(2) ^ 2.2 * X(3) ^ 4.3 + .5 * X(4) ^ -.7 * X(5) ^ -1.6 + .2 * X(6) ^ 4.3 * X(7) ^ -1.9 * X(8) ^ 8.5 <= 1

10 * X(1) ^ 2.3 * X(2) ^ 1.7 * X(3) ^ 4.5 <= 1

.6 * X(4) ^ -2.1 * X(5) ^.4 <= 1

6.2 * X(6) ^ 4.5 * X(7) ^ -2.7 * X(8) ^ -.6 <= 1

3.1 * X(1) ^ 1.6 * X(2) ^ .4 *X(3) ^ -3.8 <= 1

3.7 * X(4) ^ 5.4 * X(5) ^ 1.3 <= 1

.3 * X(6) ^ -1.1 * X(7) ^ 7.3 * X(8) ^ -5.6 <= 1

.1 <= X(j) <= 10, j=1, ..., 8.

(The superscripts above can be clearer (less confusing) below:)

0 REM DEFDBL A-Z

1 REM DEFINT I, J, K

2 DIM B(99), N(99), A(2002), G(128), J44(222), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

87 RANDOMIZE JJJJ

88 M = -3D+30

107 FOR J44 = 1 TO 8

108 A(J44) = .1 + RND * 1

109 NEXT J44

128 FOR i = 1 TO 300000

129 FOR KKQQ = 1 TO 8

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

139 FOR IPP = 1 TO FIX(1 + RND * 8)

141 B = 1 + FIX(RND * 8)

142 IF RND < 1.5 THEN 160 ELSE GOTO 167

160 r = (1 - RND * 2) * A(B)

162 X(B) = A(B) + (RND ^ (RND * 15)) * r

164 GOTO 168

167 REM IF RND < .5 THEN X(B) = A(B) - 1 ELSE X(B) = A(B) + 1

168 NEXT IPP

171 REM X(5) = (1 / (.6 * X(4) ^ -2.1)) ^ 2.5

175 X(2) = (1 / (3.1 * X(1) ^ 1.6 * X(3) ^ -3.8)) ^ 2.5

176 X(6) = (1 / (6.2 * X(7) ^ -2.7 * X(8) ^ -.6)) ^ .222222222222

177 IF 3.7 * X(4) ^ 5.4 * X(5) ^ 1.3 > 1 THEN 1670

178 IF .6 * X(4) ^ -2.1 * X(5) ^ .4 > 1 THEN 1670

179 IF 10 * X(1) ^ 2.3 * X(2) ^ 1.7 * X(3) ^ 4.5 > 1 THEN 1670

205 IF .3 * X(6) ^ -1.1 * X(7) ^ 7.3 * X(8) ^ -5.6 > 1 THEN 1670

207 IF 7.2 * X(1) ^ -3.8 * X(2) ^ 2.2 * X(3) ^ 4.3 + .5 * X(4) ^ -.7 * X(5) ^ -1.6 + .2 * X(6) ^ 4.3 * X(7) ^ -1.9 * X(8) ^ 8.5 > 1 THEN 1670

431 FOR J44 = 1 TO 8

433 IF X(J44) < .1 THEN 1670

434 IF X(J44) > 10 THEN 1670

435 NEXT J44

967 PD1 = -2 * X(1) ^ .9 * X(2) ^ -1.5 * X(3) ^ -3 - 5 * X(4) ^ -.3 * X(5) ^ 2.6 - 4.7 * X(6) ^ -1.8 * X(7) ^ -.5 * X(8)

969 P = PD1

1111 IF P <= M THEN 1670

1452 M = P

1454 FOR KLX = 1 TO 8

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1670 NEXT i

1777 IF M < -29.45 THEN 1999

1888 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -30163 is shown below:

.9817176 .193701 1.124328 .7938046 .9538843

.6856284 1.06237 .9398921 -29.42854 -30951

**.9778123 .1950181 1.123243 .7898042 .9741132 ****.7035958 1.099447 .9778958 -29.32548 -30163**

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [102], the wall-clock time **(not CPU time)** for obtaining the output through JJJJ = -30163 was 35 minutes, counting from "Starting program...". One can compare the computational results above with those in Rijckaert and Martens [76, p. 229].

The computational results presented above were obtained from the following computer system:

Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz

Installed memory (RAM): 4.00GB (3.87 GB usable)

System type: 64-bit Operating System.

**Acknowledgement**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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